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I work in a Department of Mathematics in the Irish Institute of Technology sector.

Funding for mathematics research has been reduced by the Higher Education Authority and between this, a heavy teaching load and other reasons, staff are either not very active or completely inactive in research. There are a number of departments who are very active in their research.

I am interested in exploring the idea of setting up a problem session in the institute where the research community would be invited to present problems they are having in their research that they feel mathematics department staff might be able to shed light on.

At the moment questions I have include:

  • has this been done in other institutions?
  • if yes, has it been beneficial to both communities?
  • will researchers share their problems; will the sessions sustain themselves?
  • how regularly should such a problem session take place?
  • should problems be presented at the session and solved in the next session or presented prior to the session?

I feel there are a number of obvious benefits that could come from such an endeavour and I am looking for help in seeing potential problems, etc.

I hope this question, although quite open-ended, is appropriate for this site.

Edit: Regarding the comments below

Thank you all for your help. These sessions would be primarily focussed on staff in the institute and incubated industry. I wouldn't envisage them being of the duration of a workshop: rather just a single afternoons. I am looking at something a lot less formal than the workshops ye survive. I have heard of the ESGI thank you Ruadhaí.

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  • As a non-mathematician, would something like UCLA IPAM Workshops be what you are asking about? – StrongBad Feb 1 '16 at 17:26
  • It sounds like a smaller-scale version of Oxford's Study groups with industry, a very successful program that has run dozens (hundreds?) of events all over the world; see miis.maths.ox.ac.uk/past for a partial list. – David Ketcheson Feb 1 '16 at 17:36
  • You might be interested in ESGI, in Limerick, which seems to do exactly what you ask. – R D Feb 1 '16 at 18:39
  • Thank you all for your help. These sessions would be primarily focussed on staff in the institute and incubated industry. I wouldn't envisage them being of the duration of a workshop: rather just a single afternoons. I am looking at something a lot less formal than the workshops ye survive. I have heard of the ESGI thank you Ruadhaí. – JP McCarthy Feb 2 '16 at 21:23
  • Why don't you be a resource person in mathematics – user48917 Feb 9 '16 at 5:49
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+100

From my experience (mostly on the interface of biology): unless you are thinking about something like theoretical physicists, you need to consider that most researchers will not have a good understanding of what mathematicians actually do, and will not be able to recognize an interesting mathematical problem.

This means you essentially bring the mathematicians to a state in which they will be able to identify good problems (with help of the other researchers). This is not easy, but I think it is a more sensible strategy than trying to bring the non-mathematicians to a state in which they can identify good mathematical problems (though you can nudge them in this direction).

Thus, you need to set reasonable expectations with realistic goals. I suggest the following approach:

  1. At the first stage, I would focus on introducing the mathematicians to the field, so they can start understanding the terms and what tools are being used. This will probably get the mathematicians thinking about how to introduce formality and so on. This step is also very important in order to establish a common language for discussion.
  2. Next, I would let the researchers introduce important open problems in the field. These problems don't need to be mathematically interesting - because the researchers will probably not be able to tell what is mathematically interesting anyway. This helps avoid a common issue of theorists focusing on problems that are useless for practitioners.
  3. After these are done, the participants should have the minimal set of tools to explore problems that are interesting for both sides. This should be mainly based on open discussion.

Realistically, if you are able to achieve the first 2 steps and get the people to start thinking about point 3 (as it can take some time to process all this new information) and possible establish some pre-collaborations, I would call it a success. While I strongly believe that many fields can benefit from mathematical insights, it can be very challenging to find a problem that is interesting for both sides.

BTW it may also help to invite some people which are doing active research at the interface of the two communities.

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  • Your first and second paragraphs are very insightful thank you and make point 1. key. Perhaps in point 2 I am thinking "problems in their research". Your final remark is very helpful too thank you. – JP McCarthy Feb 4 '16 at 9:46
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    I was going to answer along these lines. I am a mathematician working in social sciences and public health. I recommend that you get on the seminar mailing lists of other departments and find out what they are doing and ask questions about where they are stuck. Non-mathematicians rarely understand where mathematics (or even just mathematical thinking) would be valuable. – JenB Feb 7 '16 at 12:05
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You could set up something like a help desk or a clinic. Have a website to advertise the services to the other departments and give some examples of things you could help with. An uncomplicated way to meet is important to reduce the barrier for others to contact you. A short meeting should be enough for you to asses if this is any thing the maths department could help with.

The University of Bristol has a statistics clinic working along this way. They have a drop in sessions every other week, where researchers form other departments can present a short summary of their problem. This is not sessions where you solve problems in front of others but it is a way to facilitate collaborations.

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  • Very interesting thank you. That is more towards what I am thinking about. – JP McCarthy Feb 4 '16 at 13:56
  • Engineers won't look for academics (let alone mathematicians) as "too theoretical". You'd first have to lay groundwork, like @Bitwise's answer suggests. – vonbrand Feb 4 '16 at 17:08

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